ELECTRONIC and OPTICAL PROPERTIES of Tis2 DETERMINED from MODIFIED BECKE–JOHNSON GGA POTENTIAL (Mbj-GGA) STUDY

ACADEMIA ROMÂNĂ Rev. Roum. Chim., Revue Roumaine de Chimie 2018, 63(10), 873-880 http://web.icf.ro/rrch/ ELECTRONIC AND OPTICAL PROPERTIES OF TiS2 DETERMINED FROM MODIFIED BECKE–JOHNSON GGA POTENTIAL (mBJ-GGA) STUDY Hamza EL-KOUCH and Larbi EL FARH* Mechanics and Energetic Laboratory, Faculty of Sciences, University Mohammed 1st, Oujda, Morocco Received May 2, 2017 In this study, we report the results of electronic structure and optical properties of TiS2 calculations within the density functional theory (DFT) using the generalized gradient approximation (GGA) and an improved version of the modified Becke-Johnson (mBJ) exchange- correlation potential. The equilibrium lattice parameters and bulk modulus were found to be close to the experimentally reported results and a semi-conducting character of the material was revealed from the band structure calculation with an indirect band gap of 0.26 eV. Furthermore, DOS plots showed a prominent contribution of Ti-d, S-s and S-p. We have also calculated the dielectric function, refractive index and optical reflectivity and we have compared the obtained curves to those found experimentally by other authors. INTRODUCTION* there are many conflicting results on the electronic structure of TiS2, since it is still debated whether the Recent progress in material sciences has shown material is metallic, semi-metallic or semiconductor.8- 12 that the dimensionality of materials plays a crucial Several experimental works have reported that TiS2 role in determining their fundamental properties.1 has semiconductor behavior with a band gap ranging Especially, the two-dimensional materials, like the from 0.05 to 2.5 eV.8-10 At the same time, other 11 12 graphene, have shown rich physical properties not works classify TiS2 among metals or semi-metals observed in bulk or in the one-dimensional materials. with an indirect band gap overlap (between the points For this reason, in the latest years the properties of Γ and L in the first Brillouin zone). other 2D materials like transition-metal The aim of the present paper is to investigate dichalcogenides (TMDs) have known a renewal of the electronic, structural and optical properties of interest due to their potential applications in next- TiS2 using density functional theory (DFT) and full 2 generation nanoelectronic devices. The titanium potential linearized and augmented plane wave disulfide (TiS2) is one of those materials; it consists (FLAPW) basis set. of covalently bonded Ti and S atoms arranged in two-dimensional hexagonal planes.3 The layers are stacked together by weak Van Der Waals forces.4 COMPUTATIONAL METHODS TiS2 has been widely studied in recent years because of its use in numerous applications, particularly as a The calculations presented in this paper have cathode material in rechargeable batteries,5 as been performed within the framework of density hydrogen storage material,6 and as a high- functional theory (DFT) using the full-potential performance thermoelectric material.7 In literature, linearized augmented plane wave (FP-LAPW) * Corresponding author: [email protected]; Phone: +212628378953. 874 Hamza El-Kouch et al. method13 as implemented in the Wien2K code.14 The modified Becke-Johnson potential (mBJ) The mBJ potential for the exchange correlation as proposed by Tran and Blaha16 is: potential15 was used to calculate electronic and optical properties. mBJ BR 1 5 2tσ (r) VX ,σ ()r = CV X ,σ + (3C − 2 ) (1) π 12 ρσ ()r where C is a system-dependent parameter, with BR energy density and VX ,σ ()r is the Becke-Roussel C = 1 corresponding to the original BJ 17 N 2 (BR) potential given by: potential, ρ = σ ψ is the electronic σ ∑i=1 i,σ 1 Nσ ∗ density, tσ = ∇ψ i,σ ∇ψ i,σ is the kinetic 2 ∑i=1 BR 1 − Xσ ()r 1 − Xσ ()r VX ,σ ()r = − 1− e − X σ ()r e (2) bσ ()r 2 BR 1 VX ,σ ()r was originally proposed to mimic the 3 − X σ 3 X σ e Slater potential, the Coulomb potential bσ is calculated by: bσ = . corresponding to the exact exchange hole. 8πρσ X σ is determined from an equation involving ρσ , In eq. (1), parameter C was proposed by Tran and Blaha16, for bulk crystalline materials, by the ∇ρ , ∇ 2 ρ and t . σ σ σ following empirical relation: 1 ' 1 ∇ρ()r 2 C = −0.012 +1.023 (3) V ∫cell ρ r ' d 3r ' cell () where Vcell is the volume of the unit cell. Brillouin zone for k-space integration to achieve Larger C values than 1 lead to a less negative self-consistency. (less attractive) potential, in particular, in low- density regions. In the FP-LAPW method, a unit cell is divided RESULTS AND DISCUSSION into an interstitial zone and non-interweaving spheres known as muffin-tin (MT) of a specific 1. Structural Properties radius (RMT). Inside the MT spheres, the basis The titanium disulfide TiS has a layered sets are described by a linear combination of radial 2 hexagonal structure with space group P-3m1 (No. solutions of Schrödinger equation (for a single 164).15 One Ti atom is located at 1a (0, 0, 0) and particle and at fixed energy) along with the energy two S atoms at 2d (1/3, 2/3, 1/4) and (2/3, 1/3, 3/4) derivatives time spherical harmonics. Inside each in the unit cell, as shown in Figure 1. MT sphere, the set of basis is divided into subsets The lattice parameters and all atomic positions (core and valence). The spherically symmetric within a crystal unit cell have been relaxed in order to charge density core subsets are completely reach equilibrium configuration. The relaxation was confined inside the MT sphere. The muffin-tin radii performed simulating the XC effects by generalized RMT were chosen equal to 2.34 for Ti and 2.08 Å gradient approximation (GGA) with Perdew, Burke and Ernzerhof (PBE) parameterization. Electronic for S. The RMT*Kmax parameter was taken equal to 9. To ensure the correctness of our calculations, we structure and optical calculations were then have taken l = 10 and G = 12. Also, in the performed on this, fully relaxed structure simulating max max the XC effects by modified Becke-Johnson. This self-consistent calculations, we consider that the choice has been made due to that it has been total energy is converged to within 0.1 mRy. Note demonstrated16 that the mBJ provides a better that we have used 900 K-points in the first description of the band gaps and optical properties. Electronic and optical properties of TiS2 875 Fig. 1 – Unit cell of TiS2. Table 1 Structural parameters derived from Murnaghan-Birch equation of state 3 a (Å) b (Å) c (Å) V0[Å ] B0[GPa] B0’ E0[Ry] Present work 3.31 3.31 5.55 59.10 95.6281 4.2432 -3304.704936 Experiment 3.40718 3.40718 5.69518 57.244 45.904 9.504 Other works 51.724 58.914 4.114 In the present work the TiS2 structure was fully of S is also observed below the Fermi energy in the optimized, i.e. the lattice parameters and all the region from -5 to 0 eV. atomic positions were relaxed in order to reach the The band structure of TiS2 was calculated with values that correspond to energy minimum. The theoretical lattice parameters obtained in the results are presented in Table 1. previous section. This gait makes sense in the It is clearly seen that our lattice constant results context of a self-consistent first principle close to the experimental values with a small calculation and allows to compare the theoretical overestimation while an underestimation of bulk results at experience. The electronic band structure modulus is observed, that can be attributed to the calculated along the lines of symmetry of the general trend of PBE-GGA method which usually Brillouin zone (Figure 3) is presented in Figure 4. overestimates the lattice constant. The bulk Like for all semiconductors, they are characterized modulus (B0) is a measure of how resistant to by a band gap between the conduction band and compressibility that substance is, thus a large value the valence band. The minimum of the conduction of B0 indicates high crystal rigidity. band is located at L point and the maximum of the valence band is located at Γ point of the first 2. Electronic Properties Brillouin zone. This permits us to conclude that TiS2 is a semiconductor with indirect gap equal to To determine the nature of the electronic band 0.26 eV, which is not far of the experimental value structure, we calculated the density of states (DOS) of 0.3 eV.8 of TiS2. Thus, figure 2 shows the total and partial density of states obtained by mBJ-GGA for TiS . 2 3. Optical Properties From total DOS in Figure 2(a), we can distinguish, in the valence band, two separate In this part, we will present some optical regions. The first region, the valence lowest energy properties like dielectric function, refractive index, is due to S s-orbitals as is indicated in figure 2 (b). reflectivity, optical conductivity and absorption The second region is separated from the first by 6.7 because those calculations play a vital role in the eV. It is dominated by the Ti d and S-p orbitals in profound understanding of the nature of the the figure 2(b). Lowest conduction region located material. All these properties can be calculated above the Fermi level is formed mainly of states d from the complex dielectric function: of Ti atom with low contribution of states p of S atom. The second conduction region is separated ε(ω) = ε1(ω) + i ε2(ω) (4) from the first by 2.4 eV.

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